In order to continue on with the Real Geometry Research I wish to build a collaborative wiki to explore the Computational aspects of Real Geometry, this will then allow us to reach up into real 4-space and develop the transformations required to create a hyper-sphere.

In the process of exploring the Computational aspects of Real Geometry, I intend to make use of Python as the principal language. Over the course of the past ten years I have also used other languages and systems. For the purpose of this project I will be restricting my developments to Python, however I may publish some previous work, including a system for automatically generating Gaelic knots, written in Action Script and Flash, a system for resolving Sudoku, written in Perl and a system for developing aspects of an Animated Calculator using the methods encapsulated in Vedic Mathematics, which links Flash animations via Action Script to a core computational system in Perl or Python. This last is highly experimental and makes use of what I call ACORN, Asynchronous Computational Objects Relational Network. I cannot find this Action Script based system on my computer at the moment, but an earlier version still exists, so it will be possible to reconstruct it. It could easily be adapted to Java and C++ to facilitate other platforms. I also used this system to develop math gadgets, which could be used in the mode of Google gadgets. There may also be code snippets the Squeak flavour of SmallTalk. I also intend to migrate some of my research and design concepts from my personal Animathics R&D wiki.

For the actual development of the software in Python, I am restricted to using Python 2.3, which will suffice for the moment. At a later stage when other aspects of this project are better established it will be possible to move to a more recent version. If anyone has Python experience I would appreciate some assistance in resolving the issue of compatibility between Python 2.4, and Mac OS X Version 10.3.9 (Build 7W98). The reason for this is twofold; firstly I wish to use 1 PEP 218: Built-In Set Objects, which are in Release 2.4.3 29 March 2006, previously I had used a similar facility in Perl to develop a computational approach to resolving Sudoku, which made the software a lot more coherent; secondly my Animathics R&D wiki is on my R&D machine, and due to some changes I made in testing Python 2.4, I can no longer gain access to the material on it. The material is still there, but the Python system needs a little tweak.

References I have for Python are, Visual Quickstart Guide PYTHON, by Chris Fehily 2002, and the online book, Dive into Python. I would recommend these highly.

The three projects which I consider important for beginning the computational aspects of Real Space geometry, will be based on two books, and some of my previous research into developing a system for performing symbolic arithmetic. The first book is Kenneth William's book Triples. The development of a computational system for triples will serve the dual purpose of introducing the Python language to those who are unfamiliar with it, and also developing the more generalised aspects of triples. I have already got some of this system written, possibly in Perl, so it should be possible to make rapid progress here. The second book is Sant Kapoor's book Vedic Geometry (2004 edition). Using this book it will be possible to develop a computational system in Python, to study the transformation of a geometrical form in real 3-space into a hyper-sphere in real 4-space. Note that I do not suggest that a rotation of a sphere out of real 3-space will necessarily do the job, as I have an intuition that in order to maintain topological equivalence, with a hyper-cube some other form may be required. The last project is one I have been developing for a number of years in Perl and Python, and using Action Script and Flash for the front end. Some of this software could easily be adapted to Java platforms, thus perhaps enabling the development of a technology which will transform mobile phones into animated calculators. That way rather than just getting a result a person is shown an animation of a computational procedure. I initially intend to restrict this to 100 times, all techniques for multiplication within a one hundred square. I will explain more about this as time goes on.

In order to create a correlation of this work with modern geometry, I intend to use a number of references. The first is, Introduction to Tensor Calculus and Continuum Mechanics by J.H. Heinbockel, Department of Mathematics and Statistics, Old Dominion University. There is a link to this download-able book on the Higher-Geometry Forum. The second are a group of books I downloaded yesterday, INTRODUCTION TO VECTORS AND TENSORS, Linear and Multi-linear Algebra, Volume 1; INTRODUCTION TO VECTORS AND TENSORS, Vector and Tensor Analysis, Volume 2; by Ray M. Bowen, Mechanical Engineering, Texas A&M University, College Station, Texas and C.-C. Wang, Mathematical Sciences, Rice University, Houston, Texas: INTRODUCTION TO CONTINUUM MECHANICS FOR ENGINEERS (REVISED EDITION) 2007 By Ray M. Bowen, Professor of Mechanical Engineering, President Emeritus, Texas A&M University. This last reference will be particularly useful when we wish to examine the dynamics of real spaces, and the dynamics of the transformations in ascending to or descending from higher real spaces. In time I also hope to examine relationships with quantum mechanics and relativity, leading to a deeper understanding of the relationship between real spaces and unified field theory, but this is enough to be getting started with.

Finally of course I will be exploring aspects of the Irish language. As I mentioned previously either in an e-mail or on a post somewhere, Irish has very powerful computational characteristics. In research I completed some ten years ago, I developed a class based system for arithmetic in the Squeak flavour of SmallTalk. As part of this class based system I wrote effectively two systems, one in English, and the other in Irish. The benefits of this were enormous, as often one of the difficulties in developing a computational model, lies at the conceptual level, and I found that if I had a difficulty in comprehending a conceptual development in one language, I could use the other language to surmount this and keep moving forward. To me this is very much one of the significant aspects of vedic mathematics as well, as the multiplicity of techniques allows little breaks in the flow of knowledge to be surmounted in a number of different ways. I would highly recommend that people who have proficiency in other languages should adopt a similar procedure. Eventually we could establish a language exchange, and develop the ability to run software in our own languages on any computer in the world. I know that this can be done in Squeak, and it should also be possible in Python, and/or Perl. This also serves as a type of natural guarantor of stability in an open source system because only those familiar with the natural language will have the ability to modify the system. This is the essence of what I call Language Core Programming.

If you have any questions or queries in respect of this movement, please contact me at brian.natural.computation@gmail.com, as I will no longer be responding to e-mails in respect of this work at brian.higher.geometry@gmail.com, or brian.geometry@gmail.com.

Finally I may close down the Forum and the Google group, within a few weeks. If there is anyone willing to edit and integrate the materials on both sites, I would appreciate it if they would contact me, then the material can be placed on this site. Also if anyone has the ability to use Google sketchpad, they might also like to adapt some of the flash diagrams. In time we may want to produce animations, but static diagrams will suffice for the moment. I can provide a link for the Gaelic Fonts, also it would be useful to get a source for fonts for Devanagari. I did some work in developing fonts for Devanagari in Flash but it seems to be hiding away in my system.